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Triangles Classifying Triangles by Sides Scalene No sides congruent Isosceles 2 sides congruent Equilateral All 3 sides congruent Classifying Triangles by angles Acute Triangle Has 3 acute angles Obtuse Triangle Has one obtuse angle Right Triangle Has one right angle Triangle Sum Theorem Activity 1. Cut out the triangle given to you and label the angles with numbers. 2. Trace the triangle on your paper including the labels. 3. Rip off 2 of the 3 angles and arrange the angles to discover the interior angle sum of a triangle. 4. Paste this on top of the one you traced. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 degrees. A B mA mB mC 180 C Examples 1. Find the measure of the angle 3. Find the measure of angle A 2. Solve for x Exterior Angle Theorem Activity 1. Cut out the triangle given to you and label the angles with numbers. 2. Trace the triangle on your paper including the labels. 3. Rip off 2 of the 3 angles and arrange the angles to discover the exterior angle sum of a triangle. 4. Paste this on top of the one you traced. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. m1 mA mB 1 Examples 1. Find the measure of the indicated angle 3. Find the measure of the indicated angle 2. Solve for x Isosceles Base Angle Theorem Activity 1. On a piece of patty paper, use a compass to construct a circle. 2. Draw 2 segments from the center to the edge of the circle (radii), and connect them to create triangle ABC. 3. Fold paper so that point A maps to point C. 4. What do we notice about angle A and angle C? Base Angles Theorem If two sides of a triangle are congruent then the angles opposite those sides are congruent. A If AB AC , then B C B Converse of the Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. If B C , then AB AC. C Examples Solve for x 1. 2. 3. Midsegment Discovery Activity 1. Using a straight edge, draw a triangle. Label the vertices A, B, and C. 2. Using a compass, construct the midpoint of AB and CB. Label the midpoints D and E, respectively. 3. What do you notice about the relationship between DE and AC ? Midsegment Theorem The segment connecting the midpoints of 2 sides of a triangle is parallel to the third side A and is half as long. 1 𝐷𝐸 ∥ 𝐴𝐵 𝑎𝑛𝑑 𝐷𝐸 = 𝐴𝐵 2 B D C E Examples 1. Find the missing length indicated 3. Find the missing length indicated. 2. Solve for x